Consider the general motion of a wheel of radius 2m which can be viewed as pure translation with the velocity →v and pure rotation about O with angular velocity 5rad/s. Which of the following is incorrect?
The correct option is D→VDO=−10^j As we know, →VPQ=→ω×→rPQ So here, →VAO=ω×→rAO =5(−^k)×2(−^j)=−10^i
As we can see, the direction of velocity w.r.t O will be in negative x direction. Similarly →VBO=→ω×→rBO=5(−^k)×2(^i)=(−5×2)(^k×^i) =10m/s(−^j)=−10^j →VCO=ω×→rCO=5(−^k)×2(^j)=−10(^k×^j) =10(^i)(∵^k×^j=−^i) →VDO=ω×→rDO=5(−^k)×2(−^i)=10×(^k×^i) =10(^j) [∵^k×^i=^j] Hence, option D is incorrect.